Algorithm for constructing a convex envelope and evaluating the convexity characteristics of objects on digital images

Меденников П.А. Алгоритм построения выпуклой оболочки и оценки характеристик выпуклости объектов на цифровых изображениях // Оптический журнал. 2010. Т. 77. № 3. С. 56–59.

Medennikov P.A. Algorithm for constructing a convex envelope and evaluating the convexity characteristics of objects on digital images [in Russian] // Opticheskii Zhurnal. 2010. V. 77. № 3. P. 56–59.

P. A. Medennikov, "Algorithm for constructing a convex envelope and evaluating the convexity characteristics of objects on digital images," Journal of Optical Technology. 77(3), 198-200 (2010). https://doi.org/10.1364/JOT.77.000198

This paper presents an algorithm for constructing the convex envelope of an object, based on an analysis of the derivative of the chain code of its boundary. The construction process consists of selecting boundary points with a positive derivative that satisfy a proposed convexity condition. Such points determine the vertices of a closed polygon that is the convex envelope of the object. A method is proposed for estimating the number of holes and the convexity coefficient, based on the ratio of the perimeters of the object and of its convex envelope.